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- /*
- * Copyright (c) Contributors to the Open 3D Engine Project.
- * For complete copyright and license terms please see the LICENSE at the root of this distribution.
- *
- * SPDX-License-Identifier: Apache-2.0 OR MIT
- *
- */
- #include "EditorDefs.h"
- /**** Decompose.h - Basic declarations ****/
- typedef struct
- {
- float x, y, z, w;
- } Quatern; /* Quaternernion */
- enum QuaternPart
- {
- X, Y, Z, W
- };
- typedef Quatern HVect; /* Homogeneous 3D vector */
- typedef float HMatrix[4][4]; /* Right-handed, for column vectors */
- typedef struct
- {
- HVect t; /* Translation components */
- Quatern q; /* Essential rotation */
- Quatern u; /* Stretch rotation */
- HVect k; /* Stretch factors */
- float f; /* Sign of determinant */
- } SAffineParts;
- float polar_decomp(HMatrix M, HMatrix Q, HMatrix S);
- HVect spect_decomp(HMatrix S, HMatrix U);
- Quatern snuggle(Quatern q, HVect* k);
- /******* Matrix Preliminaries *******/
- /** Fill out 3x3 matrix to 4x4 **/
- #define mat_pad(A) (A[W][X] = A[X][W] = A[W][Y] = A[Y][W] = A[W][Z] = A[Z][W] = 0, A[W][W] = 1)
- /** Copy nxn matrix A to C using "gets" for assignment **/
- #define mat_copy(C, gets, A, n) {int i, j; for (i = 0; i < n; i++) {for (j = 0; j < n; j++) { \
- C[i][j] gets (A[i][j]); } \
- } \
- }
- /** Copy transpose of nxn matrix A to C using "gets" for assignment **/
- #define mat_tpose(AT, gets, A, n) {int i, j; for (i = 0; i < n; i++) {for (j = 0; j < n; j++) { \
- AT[i][j] gets (A[j][i]); } \
- } \
- }
- /** Assign nxn matrix C the element-wise combination of A and B using "op" **/
- #define mat_binop(C, gets, A, op, B, n) {int i, j; for (i = 0; i < n; i++) {for (j = 0; j < n; j++) { \
- C[i][j] gets (A[i][j]) op (B[i][j]); } \
- } \
- }
- /** Multiply the upper left 3x3 parts of A and B to get AB **/
- static void mat_mult(HMatrix A, HMatrix B, HMatrix AB)
- {
- int i, j;
- for (i = 0; i < 3; i++)
- {
- for (j = 0; j < 3; j++)
- {
- AB[i][j] = A[i][0] * B[0][j] + A[i][1] * B[1][j] + A[i][2] * B[2][j];
- }
- }
- }
- /** Return dot product of length 3 vectors va and vb **/
- static float vdot(float* va, float* vb)
- {
- return (va[0] * vb[0] + va[1] * vb[1] + va[2] * vb[2]);
- }
- /** Set v to cross product of length 3 vectors va and vb **/
- static void vcross(float* va, float* vb, float* v)
- {
- v[0] = va[1] * vb[2] - va[2] * vb[1];
- v[1] = va[2] * vb[0] - va[0] * vb[2];
- v[2] = va[0] * vb[1] - va[1] * vb[0];
- }
- /** Set MadjT to transpose of inverse of M times determinant of M **/
- static void adjoint_transpose(HMatrix M, HMatrix MadjT)
- {
- vcross(M[1], M[2], MadjT[0]);
- vcross(M[2], M[0], MadjT[1]);
- vcross(M[0], M[1], MadjT[2]);
- }
- /******* Quaternernion Preliminaries *******/
- /* Construct a (possibly non-unit) Quaternernion from real components. */
- static Quatern Qt_(float x, float y, float z, float w)
- {
- Quatern qq;
- qq.x = x;
- qq.y = y;
- qq.z = z;
- qq.w = w;
- return (qq);
- }
- /* Return conjugate of Quaternernion. */
- static Quatern Qt_Conj(Quatern q)
- {
- Quatern qq;
- qq.x = -q.x;
- qq.y = -q.y;
- qq.z = -q.z;
- qq.w = q.w;
- return (qq);
- }
- /* Return Quaternernion product qL * qR. Note: order is important!
- * To combine rotations, use the product Mul(qSecond, qFirst),
- * which gives the effect of rotating by qFirst then qSecond. */
- static Quatern Qt_Mul(Quatern qL, Quatern qR)
- {
- Quatern qq;
- qq.w = qL.w * qR.w - qL.x * qR.x - qL.y * qR.y - qL.z * qR.z;
- qq.x = qL.w * qR.x + qL.x * qR.w + qL.y * qR.z - qL.z * qR.y;
- qq.y = qL.w * qR.y + qL.y * qR.w + qL.z * qR.x - qL.x * qR.z;
- qq.z = qL.w * qR.z + qL.z * qR.w + qL.x * qR.y - qL.y * qR.x;
- return (qq);
- }
- /* Return product of Quaternernion q by scalar w. */
- static Quatern Qt_Scale(Quatern q, float w)
- {
- Quatern qq;
- qq.w = q.w * w;
- qq.x = q.x * w;
- qq.y = q.y * w;
- qq.z = q.z * w;
- return (qq);
- }
- /* Construct a unit Quaternernion from rotation matrix. Assumes matrix is
- * used to multiply column vector on the left: vnew = mat vold. Works
- * correctly for right-handed coordinate system and right-handed rotations.
- * Translation and perspective components ignored. */
- static Quatern Qt_FromMatrix(HMatrix mat)
- {
- /* This algorithm avoids near-zero divides by looking for a large component
- * - first w, then x, y, or z. When the trace is greater than zero,
- * |w| is greater than 1/2, which is as small as a largest component can be.
- * Otherwise, the largest diagonal entry corresponds to the largest of |x|,
- * |y|, or |z|, one of which must be larger than |w|, and at least 1/2. */
- Quatern qu = { 0.0f, 0.0f, 0.0f, 1.0f };
- double tr, s;
- tr = mat[X][X] + mat[Y][Y] + mat[Z][Z];
- if (tr >= 0.0)
- {
- s = sqrt(tr + mat[W][W]);
- qu.w = static_cast<float>(s * 0.5);
- s = 0.5 / s;
- qu.x = static_cast<float>((mat[Z][Y] - mat[Y][Z]) * s);
- qu.y = static_cast<float>((mat[X][Z] - mat[Z][X]) * s);
- qu.z = static_cast<float>((mat[Y][X] - mat[X][Y]) * s);
- }
- else
- {
- int h = X;
- if (mat[Y][Y] > mat[X][X])
- {
- h = Y;
- }
- if (mat[Z][Z] > mat[h][h])
- {
- h = Z;
- }
- switch (h)
- {
- #define caseMacro(i, j, k, I, J, K) \
- case I: \
- s = sqrt((mat[I][I] - (mat[J][J] + mat[K][K])) + mat[W][W]); \
- qu.i = static_cast<float>(s * 0.5); \
- s = 0.5 / s; \
- qu.j = static_cast<float>((mat[I][J] + mat[J][I]) * s); \
- qu.k = static_cast<float>((mat[K][I] + mat[I][K]) * s); \
- qu.w = static_cast<float>((mat[K][J] - mat[J][K]) * s); \
- break
- caseMacro(x, y, z, X, Y, Z);
- caseMacro(y, z, x, Y, Z, X);
- caseMacro(z, x, y, Z, X, Y);
- }
- }
- if (mat[W][W] != 1.0)
- {
- qu = Qt_Scale(qu, 1.0f / sqrt(mat[W][W]));
- }
- return (qu);
- }
- /******* Decomp Auxiliaries *******/
- static HMatrix mat_id = {
- {1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}
- };
- /** Compute either the 1 or infinity norm of M, depending on tpose **/
- static float mat_norm(HMatrix M, int tpose)
- {
- int i;
- float sum, max;
- max = 0.0;
- for (i = 0; i < 3; i++)
- {
- if (tpose)
- {
- sum = fabs(M[0][i]) + fabs(M[1][i]) + fabs(M[2][i]);
- }
- else
- {
- sum = fabs(M[i][0]) + fabs(M[i][1]) + fabs(M[i][2]);
- }
- if (max < sum)
- {
- max = sum;
- }
- }
- return max;
- }
- static float norm_inf(HMatrix M) {return mat_norm(M, 0); }
- static float norm_one(HMatrix M) {return mat_norm(M, 1); }
- /** Return index of column of M containing maximum abs entry, or -1 if M=0 **/
- static int find_max_col(HMatrix M)
- {
- float abs, max;
- int i, j, col;
- max = 0.0;
- col = -1;
- for (i = 0; i < 3; i++)
- {
- for (j = 0; j < 3; j++)
- {
- abs = M[i][j];
- if (abs < 0.0)
- {
- abs = -abs;
- }
- if (abs > max)
- {
- max = abs;
- col = j;
- }
- }
- }
- return col;
- }
- /** Setup u for Household reflection to zero all v components but first **/
- static void make_reflector(float* v, float* u)
- {
- float s = sqrt(vdot(v, v));
- u[0] = v[0];
- u[1] = v[1];
- u[2] = v[2] + ((v[2] < 0.0) ? -s : s);
- s = static_cast<float>(sqrt(2.0f / vdot(u, u)));
- u[0] = u[0] * s;
- u[1] = u[1] * s;
- u[2] = u[2] * s;
- }
- /** Apply Householder reflection represented by u to column vectors of M **/
- static void reflect_cols(HMatrix M, float* u)
- {
- int i, j;
- for (i = 0; i < 3; i++)
- {
- float s = u[0] * M[0][i] + u[1] * M[1][i] + u[2] * M[2][i];
- for (j = 0; j < 3; j++)
- {
- M[j][i] -= u[j] * s;
- }
- }
- }
- /** Apply Householder reflection represented by u to row vectors of M **/
- static void reflect_rows(HMatrix M, float* u)
- {
- int i, j;
- for (i = 0; i < 3; i++)
- {
- float s = vdot(u, M[i]);
- for (j = 0; j < 3; j++)
- {
- M[i][j] -= u[j] * s;
- }
- }
- }
- /** Find orthogonal factor Q of rank 1 (or less) M **/
- static void do_rank1(HMatrix M, HMatrix Q)
- {
- float v1[3], v2[3], s;
- int col;
- mat_copy(Q, =, mat_id, 4);
- /* If rank(M) is 1, we should find a non-zero column in M */
- col = find_max_col(M);
- if (col < 0)
- {
- return; /* Rank is 0 */
- }
- v1[0] = M[0][col];
- v1[1] = M[1][col];
- v1[2] = M[2][col];
- make_reflector(v1, v1);
- reflect_cols(M, v1);
- v2[0] = M[2][0];
- v2[1] = M[2][1];
- v2[2] = M[2][2];
- make_reflector(v2, v2);
- reflect_rows(M, v2);
- s = M[2][2];
- if (s < 0.0)
- {
- Q[2][2] = -1.0;
- }
- reflect_cols(Q, v1);
- reflect_rows(Q, v2);
- }
- /** Find orthogonal factor Q of rank 2 (or less) M using adjoint transpose **/
- static void do_rank2(HMatrix M, HMatrix MadjT, HMatrix Q)
- {
- float v1[3], v2[3];
- float w, x, y, z, c, s, d;
- int col;
- /* If rank(M) is 2, we should find a non-zero column in MadjT */
- col = find_max_col(MadjT);
- if (col < 0)
- {
- do_rank1(M, Q);
- return;
- } /* Rank<2 */
- v1[0] = MadjT[0][col];
- v1[1] = MadjT[1][col];
- v1[2] = MadjT[2][col];
- make_reflector(v1, v1);
- reflect_cols(M, v1);
- vcross(M[0], M[1], v2);
- make_reflector(v2, v2);
- reflect_rows(M, v2);
- w = M[0][0];
- x = M[0][1];
- y = M[1][0];
- z = M[1][1];
- if (w * z > x * y)
- {
- c = z + w;
- s = y - x;
- d = sqrt(c * c + s * s);
- c = c / d;
- s = s / d;
- Q[0][0] = Q[1][1] = c;
- Q[0][1] = -(Q[1][0] = s);
- }
- else
- {
- c = z - w;
- s = y + x;
- d = sqrt(c * c + s * s);
- c = c / d;
- s = s / d;
- Q[0][0] = -(Q[1][1] = c);
- Q[0][1] = Q[1][0] = s;
- }
- Q[0][2] = Q[2][0] = Q[1][2] = Q[2][1] = 0.0;
- Q[2][2] = 1.0;
- reflect_cols(Q, v1);
- reflect_rows(Q, v2);
- }
- /******* Polar Decomposition *******/
- /* Polar Decomposition of 3x3 matrix in 4x4,
- * M = QS. See Nicholas Higham and Robert S. Schreiber,
- * Fast Polar Decomposition of An Arbitrary Matrix,
- * Technical Report 88-942, October 1988,
- * Department of Computer Science, Cornell University.
- */
- float polar_decomp(HMatrix M, HMatrix Q, HMatrix S)
- {
- #define TOL 1.0e-6
- HMatrix Mk, MadjTk, Ek;
- float det, M_one, M_inf, MadjT_one, MadjT_inf, E_one, gamma, g1, g2;
- mat_tpose(Mk, =, M, 3);
- M_one = norm_one(Mk);
- M_inf = norm_inf(Mk);
- do
- {
- adjoint_transpose(Mk, MadjTk);
- det = vdot(Mk[0], MadjTk[0]);
- if (det == 0.0)
- {
- do_rank2(Mk, MadjTk, Mk);
- break;
- }
- MadjT_one = norm_one(MadjTk);
- MadjT_inf = norm_inf(MadjTk);
- gamma = sqrt(sqrt((MadjT_one * MadjT_inf) / (M_one * M_inf)) / fabs(det));
- g1 = gamma * 0.5f;
- g2 = 0.5f / (gamma * det);
- mat_copy(Ek, =, Mk, 3);
- mat_binop(Mk, =, g1 * Mk, +, g2 * MadjTk, 3);
- mat_copy(Ek, -=, Mk, 3);
- E_one = norm_one(Ek);
- M_one = norm_one(Mk);
- M_inf = norm_inf(Mk);
- } while (E_one > (M_one * TOL));
- mat_tpose(Q, =, Mk, 3);
- mat_pad(Q);
- mat_mult(Mk, M, S);
- mat_pad(S);
- for (int i = 0; i < 3; i++)
- {
- for (int j = i; j < 3; j++)
- {
- S[i][j] = S[j][i] = 0.5f * (S[i][j] + S[j][i]);
- }
- }
- return (det);
- }
- /******* Spectral Decomposition *******/
- /* Compute the spectral decomposition of symmetric positive semi-definite S.
- * Returns rotation in U and scale factors in result, so that if K is a diagonal
- * matrix of the scale factors, then S = U K (U transpose). Uses Jacobi method.
- * See Gene H. Golub and Charles F. Van Loan. Matrix Computations. Hopkins 1983.
- */
- HVect spect_decomp(HMatrix S, HMatrix U)
- {
- HVect kv;
- double Diag[3], OffD[3]; /* OffD is off-diag (by omitted index) */
- double g, h, fabsh, fabsOffDi, t, theta, c, s, tau, ta, OffDq, a, b;
- static char nxt[] = {Y, Z, X};
- int sweep;
- mat_copy(U, =, mat_id, 4);
- Diag[X] = S[X][X];
- Diag[Y] = S[Y][Y];
- Diag[Z] = S[Z][Z];
- OffD[X] = S[Y][Z];
- OffD[Y] = S[Z][X];
- OffD[Z] = S[X][Y];
- for (sweep = 20; sweep > 0; sweep--)
- {
- float sm = static_cast<float>(fabs(OffD[X]) + fabs(OffD[Y]) + fabs(OffD[Z]));
- if (sm == 0.0)
- {
- break;
- }
- for (int i = Z; i >= X; i--)
- {
- int p = nxt[i];
- int q = nxt[p];
- fabsOffDi = fabs(OffD[i]);
- g = 100.0 * fabsOffDi;
- if (fabsOffDi > AZ::Constants::FloatEpsilon)
- {
- h = Diag[q] - Diag[p];
- fabsh = fabs(h);
- if (fabsh + g == fabsh)
- {
- t = OffD[i] / h;
- }
- else
- {
- theta = 0.5 * h / OffD[i];
- t = 1.0 / (fabs(theta) + sqrt(theta * theta + 1.0));
- if (theta < 0.0)
- {
- t = -t;
- }
- }
- c = 1.0 / sqrt(t * t + 1.0);
- s = t * c;
- tau = s / (c + 1.0);
- ta = t * OffD[i];
- OffD[i] = 0.0;
- Diag[p] -= ta;
- Diag[q] += ta;
- OffDq = OffD[q];
- OffD[q] -= s * (OffD[p] + tau * OffD[q]);
- OffD[p] += s * (OffDq - tau * OffD[p]);
- for (int j = Z; j >= X; j--)
- {
- a = U[j][p];
- b = U[j][q];
- U[j][p] -= static_cast<float>(s * (b + tau * a));
- U[j][q] += static_cast<float>(s * (a - tau * b));
- }
- }
- }
- }
- kv.x = static_cast<float>(Diag[X]);
- kv.y = static_cast<float>(Diag[Y]);
- kv.z = static_cast<float>(Diag[Z]);
- kv.w = 1.0f;
- return (kv);
- }
- /******* Spectral Axis Adjustment *******/
- /* Given a unit Quaternernion, q, and a scale vector, k, find a unit Quaternernion, p,
- * which permutes the axes and turns freely in the plane of duplicate scale
- * factors, such that q p has the largest possible w component, i.e. the
- * smallest possible angle. Permutes k's components to go with q p instead of q.
- * See Ken Shoemake and Tom Duff. Matrix Animation and Polar Decomposition.
- * Proceedings of Graphics Interface 1992. Details on p. 262-263.
- */
- Quatern snuggle(Quatern q, HVect* k)
- {
- #define SQRTHALF (0.7071067811865475244f)
- #define sgn(n, v) ((n) ? -(v) : (v))
- #define swap(a, i, j) {a[3] = a[i]; a[i] = a[j]; a[j] = a[3]; }
- #define cycle(a, p) if (p) {a[3] = a[0]; a[0] = a[1]; a[1] = a[2]; a[2] = a[3]; } \
- else {a[3] = a[2]; a[2] = a[1]; a[1] = a[0]; a[0] = a[3]; }
- Quatern p = { 0.0f, 0.0f, 0.0f, 1.0f };
- float ka[4];
- int i, turn = -1;
- ka[X] = k->x;
- ka[Y] = k->y;
- ka[Z] = k->z;
- if (ka[X] == ka[Y])
- {
- if (ka[X] == ka[Z])
- {
- turn = W;
- }
- else
- {
- turn = Z;
- }
- }
- else
- {
- if (ka[X] == ka[Z])
- {
- turn = Y;
- }
- else if (ka[Y] == ka[Z])
- {
- turn = X;
- }
- }
- if (turn >= 0)
- {
- Quatern qtoz, qp;
- unsigned neg[3], win;
- double mag[3], t;
- static Quatern qxtoz = {0, SQRTHALF, 0, SQRTHALF};
- static Quatern qytoz = {SQRTHALF, 0, 0, SQRTHALF};
- static Quatern qppmm = { 0.5, 0.5, -0.5, -0.5};
- static Quatern qpppp = { 0.5, 0.5, 0.5, 0.5};
- static Quatern qmpmm = {-0.5, 0.5, -0.5, -0.5};
- static Quatern qpppm = { 0.5, 0.5, 0.5, -0.5};
- static Quatern q0001 = { 0.0, 0.0, 0.0, 1.0};
- static Quatern q1000 = { 1.0, 0.0, 0.0, 0.0};
- switch (turn)
- {
- default:
- return (Qt_Conj(q));
- case X:
- q = Qt_Mul(q, qtoz = qxtoz);
- swap(ka, X, Z);
- break;
- case Y:
- q = Qt_Mul(q, qtoz = qytoz);
- swap(ka, Y, Z);
- break;
- case Z:
- qtoz = q0001;
- break;
- }
- q = Qt_Conj(q);
- mag[0] = (double)q.z * q.z + (double)q.w * q.w - 0.5;
- mag[1] = (double)q.x * q.z - (double)q.y * q.w;
- mag[2] = (double)q.y * q.z + (double)q.x * q.w;
- for (i = 0; i < 3; i++)
- {
- neg[i] = (mag[i] < 0.0);
- if (neg[i])
- {
- mag[i] = -mag[i];
- }
- }
- if (mag[0] > mag[1])
- {
- if (mag[0] > mag[2])
- {
- win = 0;
- }
- else
- {
- win = 2;
- }
- }
- else
- {
- if (mag[1] > mag[2])
- {
- win = 1;
- }
- else
- {
- win = 2;
- }
- }
- switch (win)
- {
- case 0:
- if (neg[0])
- {
- p = q1000;
- }
- else
- {
- p = q0001;
- } break;
- case 1:
- if (neg[1])
- {
- p = qppmm;
- }
- else
- {
- p = qpppp;
- } cycle(ka, 0);
- break;
- case 2:
- if (neg[2])
- {
- p = qmpmm;
- }
- else
- {
- p = qpppm;
- } cycle(ka, 1);
- break;
- }
- qp = Qt_Mul(q, p);
- t = sqrt(mag[win] + 0.5);
- p = Qt_Mul(p, Qt_(0.0f, 0.0f, static_cast<float>(-qp.z / t), static_cast<float>(qp.w / t)));
- p = Qt_Mul(qtoz, Qt_Conj(p));
- }
- else
- {
- float qa[4], pa[4];
- unsigned lo, hi, neg[4], par = 0;
- double all, big, two;
- qa[0] = q.x;
- qa[1] = q.y;
- qa[2] = q.z;
- qa[3] = q.w;
- for (i = 0; i < 4; i++)
- {
- pa[i] = 0.0;
- neg[i] = (qa[i] < 0.0);
- if (neg[i])
- {
- qa[i] = -qa[i];
- }
- par ^= neg[i];
- }
- /* Find two largest components, indices in hi and lo */
- if (qa[0] > qa[1])
- {
- lo = 0;
- }
- else
- {
- lo = 1;
- }
- if (qa[2] > qa[3])
- {
- hi = 2;
- }
- else
- {
- hi = 3;
- }
- if (qa[lo] > qa[hi])
- {
- if (qa[lo ^ 1] > qa[hi])
- {
- hi = lo;
- lo ^= 1;
- }
- else
- {
- hi ^= lo;
- lo ^= hi;
- hi ^= lo;
- }
- }
- else
- {
- if (qa[hi ^ 1] > qa[lo])
- {
- lo = hi ^ 1;
- }
- }
- all = (qa[0] + qa[1] + qa[2] + qa[3]) * 0.5;
- two = (qa[hi] + qa[lo]) * SQRTHALF;
- big = qa[hi];
- if (all > two)
- {
- if (all > big)/*all*/
- {
- {
- int ii;
- for (ii = 0; ii < 4; ii++)
- {
- pa[ii] = static_cast<float>(sgn(neg[ii], 0.5f));
- }
- }
- cycle(ka, par)
- }
- else
- { /*big*/
- pa[hi] = static_cast<float>(sgn(neg[hi], 1.0f));
- }
- }
- else
- {
- if (two > big)/*two*/
- {
- pa[hi] = sgn(neg[hi], SQRTHALF);
- pa[lo] = sgn(neg[lo], SQRTHALF);
- if (lo > hi)
- {
- hi ^= lo;
- lo ^= hi;
- hi ^= lo;
- }
- if (hi == W)
- {
- hi = "\001\002\000"[lo];
- lo = 3 - hi - lo;
- }
- swap(ka, hi, lo)
- }
- else
- { /*big*/
- pa[hi] = static_cast<float>(sgn(neg[hi], 1.0f));
- }
- }
- p.x = -pa[0];
- p.y = -pa[1];
- p.z = -pa[2];
- p.w = pa[3];
- }
- k->x = ka[X];
- k->y = ka[Y];
- k->z = ka[Z];
- return (p);
- }
- /******* Decompose Affine Matrix *******/
- /* Decompose 4x4 affine matrix A as TFRUK(U transpose), where t contains the
- * translation components, q contains the rotation R, u contains U, k contains
- * scale factors, and f contains the sign of the determinant.
- * Assumes A transforms column vectors in right-handed coordinates.
- * See Ken Shoemake and Tom Duff. Matrix Animation and Polar Decomposition.
- * Proceedings of Graphics Interface 1992.
- */
- static void decomp_affine(HMatrix A, SAffineParts* parts)
- {
- HMatrix Q, S, U;
- Quatern p;
- float det;
- parts->t = Qt_(A[X][W], A[Y][W], A[Z][W], 0);
- det = polar_decomp(A, Q, S);
- if (det < 0.0)
- {
- mat_copy(Q, =, -Q, 3);
- parts->f = -1;
- }
- else
- {
- parts->f = 1;
- }
- parts->q = Qt_FromMatrix(Q);
- parts->k = spect_decomp(S, U);
- parts->u = Qt_FromMatrix(U);
- p = snuggle(parts->u, &parts->k);
- parts->u = Qt_Mul(parts->u, p);
- }
- static void spectral_decomp_affine(HMatrix A, SAffineParts* parts)
- {
- HMatrix Q, S, U;
- float det;
- parts->t = Qt_(A[X][W], A[Y][W], A[Z][W], 0);
- det = polar_decomp(A, Q, S);
- if (det < 0.0)
- {
- mat_copy(Q, =, -Q, 3);
- parts->f = -1;
- }
- else
- {
- parts->f = 1;
- }
- parts->q = Qt_FromMatrix(Q);
- parts->k = spect_decomp(S, U);
- parts->u = Qt_FromMatrix(U);
- }
- // Decompose matrix to affine parts.
- void AffineParts::Decompose(const Matrix34& tm)
- {
- SAffineParts parts;
- Matrix44 tm44(tm);
- HMatrix& H = *((HMatrix*)&tm44); // Treat HMatrix as a Matrix44.
- decomp_affine(H, &parts);
- rot = Quat(parts.q.w, parts.q.x, parts.q.y, parts.q.z);
- rotScale = Quat(parts.u.w, parts.u.x, parts.u.y, parts.u.z);
- pos = Vec3(parts.t.x, parts.t.y, parts.t.z);
- scale = Vec3(parts.k.x, parts.k.y, parts.k.z);
- fDet = parts.f;
- }
- // Spectral matrix decompostion to affine parts.
- void AffineParts::SpectralDecompose(const Matrix34& tm)
- {
- SAffineParts parts;
- Matrix44 tm44(tm);
- HMatrix& H = *((HMatrix*)&tm44); // Treat HMatrix as a Matrix44.
- spectral_decomp_affine(H, &parts);
- rot = Quat(parts.q.w, parts.q.x, parts.q.y, parts.q.z);
- rotScale = Quat(parts.u.w, parts.u.x, parts.u.y, parts.u.z);
- pos = Vec3(parts.t.x, parts.t.y, parts.t.z);
- scale = Vec3(parts.k.x, parts.k.y, parts.k.z);
- fDet = parts.f;
- }
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